Known carbon fiber fabrics comprise a web of thin filaments of carbon fibers arranged perpendicularly to each other. These known fabrics are impregnated with polymeric resins and overlapped according to suitable directions. The resins are cured to obtain rigid materials with a high specific resistance, which are suitable for the production of structural parts or aesthetic parts. These materials, because of their stiffness characteristic, cannot be applied for example to the internal parts of motor vehicles, where flexible fabrics that can be sewn and folded are required. This also excludes the use of raw fabrics made of carbon fiber, which tend to unthread and are not able to keep unchanged the arrangement of the fibers once deformed.